Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-9x-y &= -2 \\ 9x-9y &= -8\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-9y = -9x-8$ Divide both sides by $-9$ to isolate $y$ $y = {x + \dfrac{8}{9}}$ Substitute this expression for $y$ in the first equation. $-9x-({x + \dfrac{8}{9}}) = -2$ $-9x - x - \dfrac{8}{9} = -2$ Simplify by combining terms, then solve for $x$ $-10x - \dfrac{8}{9} = -2$ $-10x = -\dfrac{10}{9}$ $x = \dfrac{1}{9}$ Substitute $\dfrac{1}{9}$ for $x$ back into the top equation. $-9( \dfrac{1}{9})-y = -2$ $-1-y = -2$ $-y = -1$ $y = 1$ The solution is $\enspace x = \dfrac{1}{9}, \enspace y = 1$.